Expand the Advanced Options part and select Transparency from the "Fill with" drop down list, as shown in picture Adding a transparent 4x4 image.

Press the + key several times to zoom the image you've just created until it is big enough for you to work in it.

We are going to paint now one pixel at a time. For doing this:

Select the pencil tool from the toolbox

Keep the opacity at 100%

Select the Circle (01) brush, and keep its scale at 1.00, as shown in picture Pencil settings

Paint the top row:

Set the Foregound colour to 4c4c4c and paint the top left pixel.

Set the Foreground colour to 494949 and paint the second pixel of the top row.

Set the Foreground colour to 252525 and paint the third pixel of the top row.

Set the Foreground colour to 232323 and paint the last pixel of the top row.

Repeat the process to paint the second row, by setting each pixel with the following colours:

Set the Foreground colour to 383838 for the first pixel.

Set the Foreground colour to 373737 for the second pixel.

Set the Froreground colour to 101010 for the third pixel.

Set the Foreground colour to 0f0f0f for the last pixel. Your image will now look like the one in picture First two rows

For the third and fourth rows we are going to use the same colours we've used but in different order.

Paint the third row:

Set the Foreground colour to 252525 and paint the first pixel.

Set the Foreground colour to 232323 and paint the second pixel.

Set the Foreground colour to 4c4c4c and paint the third pixel.

Set the Froreground colour to 494949 and paint the last pixel.

Paint the last row:

Set the Foreground colour to 101010 and paint the first pixel.

Set the Foreground colour to 0f0f0f and paint the second pixel.

Set the Foreground colour to 383838 and paint the third pixel.

Set the Foreground colour to 373737 and paint the last bottom pixel.

In picture Colours used in each of the pixels you have the numeric values of the colours that we have used to paint each of the pixels of our image.

Now we are going to save the image as a pattern:

Select the menu option File -> Save as

Enter a name for the file with extension .pat (for example, CarbonFiber.pat)

Save it to the folder \Program Files\GIMP-2.0\share\gimp\2.0\patterns\

After pressing the Save button a window will pop up asking for a description. Enter a suitable one like Carbon Fiber (this desription is what you will see in GIMP when browsing your installed patterns, so enter something meaningful).

Next step is to make GIMP to load the new pattern we've just created:

Select the Bucket Fill tool from the Toolbox as shown in picture Adding the pattern to GIMP.

Select the Pattern Fill option

Click on the pattern little square image and a window will be displayed showing all installed patterns.

Click on the little bucket icon at the bottom right corner of the available patterns window and this will open the Patterns dialog as shown in picture Patterns dialog.

Click on the Refresh patterns button (the two circular arrows icon) and wait while GIMP adds all the new patterns it finds to the list.

Close the Patterns dialog and now the Carbon Fiber pattern will be available.

Use the pattern to create a Carbon fiber texture

Basic Carbon fiber texture

Create a new image.

Select the Bucket Fill tool from the Toolbox as shown in picture Adding the pattern to GIMP.

Select the Pattern Fill option

Click on the pattern little square image and a window will be displayed showing all installed patterns.

Select the Carbon Fiber pattern you've just created from the list.

Fill the image with the pattern and you'll get a texture like the one swhon in picture Basic Carbon fiber texture.